Transformerless synthesis of transistor and thyristor switching RLC 1-ports

As an extension of the synthesis method developed in a previous paper, the transformerless synthesis of reciprocal switched 1-ports is presented in this paper. the transformerless structures of resistance switching n-ports described by impedance, admittance or hybrid matrices have been proposed. These structures enable the synthesis of dynamical switching RC, RL and RLC 1-ports. Using the state variables method, the realizability conditions and identification formulae for constant and sinusoidal input functions have been derived. Three numerical examples illustrate the developed methods. the present theory can be applied to create new thyristor and transistor arrangements, particularly compensators and auxiliary switching LC circuits facilitating the commutation of thyristors and transistors.     

On the passivity criterion for lti N-ports

Existing proofs of the passivity criterion for linear, time-invariant, distributed N-ports are either incorrect or too involved, requiring the use of advanced mathematics such as distribution theory. This paper presents a simple but completely rigorous proof using only basic real and complex analysis. For the sake of completeness we have included simple proofs of the Paley-Wiener theorem and the Poisson formula for the half plane. We show that solvability, a non-intuitive technical assumption made in rigorous theories of LTI passive networks, is virtually always satisfied. Finally, we give a passivity criterion applicable to N-ports described by general co-ordinates, from which passivity criteria for any specific representation (e.g. impedance, admittance, hybrid, transmission, scattering, etc.) can be trivially derived.     

A possibility of filling the gap between local and global passivity of non-linear networks and some of its consequences

In the qualitative theory of non-linear networks the non-linear n-ports are generally considered either locally passive or globally passive even eventually globally passive (the most restrictive or the least restrictive properties respectively). Moreover the reciprocity condition in many cases (e.g. complete stability) restricts the area of applications. In the area of economics and other fields, basically motivated by Sandberg's results, the role of the off-diagonally monotone and antitone mappings is crucial. In this paper, based on the above facts and results, it is shown that partly similar classes of mappings could have a role in non-linear network theory. More precisely, the off-diagonally locally active (passive) n-ports, defined in the paper, could represent an important new class of n-ports. As an application of the features of this new class of n-ports two Theorems are given showing conditions under which in case of a network consisting of off-diagonally locally active n-ports the DC solution can be uniquely calculated using the standard iterative methods and an autonomous network is asymptotically stable in a given domain. Hence, this paper partially overcomes the so called ‘curse of non-reciprocity’.     

D–T adaptor: Applications to the design of non-linear N-ports

A new network element is presented which can be of interest for synthesizing non-linear n-ports. It is shown that the use of n D–T adaptors reduces the problem to the synthesis of a multidimensional transfer-characteristic (TC) plot. Some examples are given to show the applicability of the procedure and its ability to make a convenient use of integrated technology.     

Existence of hybrid matrices for active n-ports encountered in the analysis of transistor networks

It is shown that hybrid matrices exist for certain types of active n-ports constructed using resistors and controlled sources. Furthermore, it is shown that the existence of these hybrid matrices implies that a certain well-known set of necessary and sufficient conditions, which guarantees the uniqueness of solutions to the nonlinear DC equations of transistor networks, can be simplified. Additional results are presented which show how the amount of computation required to verify these conditions can be reduced.     

Sufficient conditions for the unique solvability of linear networks containing memoryless 2-ports

Combinatorial necessary and sufficient conditions for the unique solvability of linear networks containing n-ports are well known for the ‘general’ case. They are only necessary if relations among n-port parameters are also taken into consideration. In the present paper combinatorial sufficient conditions are presented for linear networks containing RLC elements and memoryless 2-ports. The somewhat surprising result is proved that whether a 2-port can cause certain types of singularities can be predicted before the interconnection. A concept, similar to the normal tree (which intersects ideal transformers by one, gyrators by two or no edges) is introduced for arbitrary 2-ports. Its existence implies unique solvability. Relations to previous results and algorithmical aspects are also discussed.     

Topologie des kopplungsfreien Reaktanz-2n-Poles mit geringstem Aufwand an Speichern

Übersicht In dieser Arbeit werden Kriterien abgeleitet, die cs erlauben, an einem vorgelegten kopplungsfreien Reaktanz-2n Pol die Zahl der überflüssigen Spulen und Kondensatoren zu ermitteln. Ausgangspunkt der Untersuchungen ist die im 2. Kapitel dargestellte Maschenimpedanzmatrix eines Reaktanz-2n-Poles und deren lineare Transformation in die Matrix einer äquivalenten Schaltung. Im 3. Kapitel wird ein Zusammenhang zwischen der geringsten Zahl von Spulen und Kondensatoren und topologischen Größen aufgezeigt. Im letzten Kapitel werden Erweiterungen der gewonnenen Sätze dargestellt.

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Summary Criteria will be deduced, which permit to find out the number of superfluous coils and capacitors in a linear and losslessn-port without magnetic couplings. The investigation starts with the loop impedance matrix of a losslessn-port and its linear transformation in the matrix of an equivalent circuit. This is described in the second chapter. In the third chapter relations are to be presented between the minimum number of coils and capacitors and topological structures. Some extensions of the won theorems, especially on the invariance of the minimum number of coils and the minimum number of capacitors in equivalentn-ports, are given in the last chapter.

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Mit 2 Textabbildungen     

Experimental studies on realization of fractional inductors and fractional‐order bandpass filters

This paper presents the hardware realization and performance study of fractional inductors of order 0 < α < 2. The fractional inductors used in this work have been realized with the help of general impedance converter circuit and fractional capacitors. Impedance characterization of fractional inductors with different exponents has been carried out experimentally. Also a generalized approach to design a fractional‐order bandpass filter is discussed in this work. The fractional‐order bandpass filter consists of a series combination of a resistor, a fractional inductor of order 1 < α < 2, and a fractional capacitor of order 0 < β < 1. The performance of fractional‐order bandpass filters has been studied and compared with corresponding integer‐order filters through both experimentation and simulation. Copyright © 2014 John Wiley & Sons, Ltd.     

Envelope analysis of nonlinear electronic circuits based on harmonic balance method

We propose here a Spice‐oriented envelope analysis based on the HB (harmonic balance) method, where Fourier coefficients are assumed to be slowly varying. The Fourier expansions of nonlinear devices are executed by MATLAB in the symbolic forms. In this time, the nonlinearities need to be approximated by the polynomial functions. The determining equation of the HB method is formulated as Sine–Cosine circuit in the form of schematic diagram using ABMs (analog behavior models) of Spice. Each sub‐circuit corresponding to the higher harmonic component is almost the same circuit topology as the original one and has dynamic elements such as capacitors and inductors. The Sine–Cosine circuit can be solved by the transient analysis of Spice. Thus, our method is rather a symbolic approach in the meaning that the HB determining equation is given by the schematic diagram of Spice. Our method can be easily applied to the analysis of middle order of nonlinear communication circuits such as mixers and amplitude modulators and to the analysis of interesting phenomena in the nonlinear oscillations. After many simulation experiments, the results show that our envelope analysis is about 50 times faster than the direct transient analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

Cascade decomposition of a passive 2n-port network

This paper deals with a cascade decomposition of a passive 2n-port network. after a basic discussion relative to complex- and unit-normalized scattering matrices, necessary and sufficient conditions are presented under which given lossless 2n-ports D₁ and D₂ are simultaneously extractable from the front- and back-ends of the passive 2n-port N, respectively, to leave a passive 2n-port remainder Ne. Based on these conditions, some relations between the individual and simultaneous extractability of D₁ and D₂ from N for both degenerate and non-degenerate remainders N_e are discussed. the results are presented in terms of scattering as well as impedance matrices and can be considered as an extension of those given in Reference 1.     

Double broadband matching and the problem of reciprocal reactance 2n-port cascade decomposition

Let N, N₁, N₂ and N₃ be prescribed reciprocal reactance 2n-ports. Then, under certain mild restrictions, this paper supplies answers to the following two related problems:. P₁. Find the necessary and sufficient conditions for the physical extractability of N₁ from the front-end of N. P₂. Given that N₂ and N₃ are individually physically extractable from the back and front-ends of N. respectively, find a set of sharp sufficient conditions for their simulations physical extractability from N. The criteria are formulated in terms of the associated scattering matrices and are reasonably simple to apply. Moreover, they also have a clear-cut network significance involving transmission zeros. to illustrate their use, a recent result for the design of non-degenerate double broadband-matching equalizers⁶ is generalized to a 2n-port setting in Theorem 2, corollary 2. Lastly, to round out the development, impedance versions of both Theorem 1 and Theorem 2, corollary 2, are presented in Section 2. This restatement is accomplished with the aid of a new Darlington 2n-port embedding for passive reciprocal n-ports that is phrased entirely in the language of impedance matrices.     

The generalized tree for state variables in linear active networks

A tree for the association of state variables in linear active networks is presented. This tree is selected in such a manner that the voltages across the capacitors contained in it and the currents through the inductors contained in its cotree may be chosen as state variables of a linear network. An algorithm for finding such a tree is given, and the association of state variables with this tree are demonstrated by examples.     

Uniqueness of the steady state for small source amplitudes in non-linear non-autonomous circuitsc

The purpose of this paper is to give a sufficient condition for the uniqueness of the steady state for circuits that are composed of strictly locally passive capacitors and inductors, of time-dependent bounded voltage and current sources and of a resistive N-port that is strictly locally passive and eventually strictly passive. It is an extension of previously obtained results by the same authors, where strong local passivity was required. the new condition allows one to give a bound on the source amplitudes below which passive elements. It also gives a more explicit content to a theorem by Chua and Green which states that for sufficiently small source amplitudes the steady state is unique. the new condition is obtained by giving explicit uniform eventual bounds on the solutions as ^t → ∞, which are of independent interest. Two examples illustrate that the various explicit bounds can easily be computed in concrete examples.     

Design of multi-band multi-section transmission line transformer using particle swarm optimization

The design of N _t -section matching transformer operating at N _t arbitrary frequencies using the particle swarm optimization (PSO) method is presented. Although analytical methods based on standard transmission line theory can be used in such designs, however, the analysis becomes cumbersome if N _t exceeds two, and numerical methods should be used to solve the resulting nonlinear equations. The design using the PSO, however, is much easier, and gives the same results as the analytical methods. Different examples are presented and compared with published literature.     

Lossless 2-ports between non-reactive terminations

Lossless reciprocal 2-ports between terminations with even impedance functions are considered. They are the unifying concept for the synthesis of FDNR and leapfrog RC-active filters in their most general form. The scattering matrix of lossless reciprocal 2-ports with respect to such terminations is defined, its canonic form deduced and the transfer of active power discussed. This scattering matrix is related to the usual scattering matrix of the same 2-port but with respect to unit resistance terminations. In such a way the precise structure of the 2-port as an LC ladder can be deduced from properties of the original transfer function and the termination impedances and the LC synthesis can be performed by conventional methods and programs. An exhaustive enumeration of the different cases that may arise is given. It can give a general outlook on the different RC-active filters that may be obtained.     

New theorems in the synthesis of passive multiplexers

Coupling networks that divide the frequency spectrum into separate frequency bands and also provide desired filtering are known as multiplexers. In this paper we present four new theorems concerning the synthesis-theoretic structure of lumped passive multiplexers constructed as lossless reciprocal n-ports. In particular we prove in Theorem 1 that any set of n – 1 admissible power gains, complementary or otherwise, can be realized by a series interconnection of n–1 appropriately chosen non-Foster positive-real functions. In Theorems 2–4 we establish various necessary and sufficient conditions for the realization of bounded-real gains s₂₁(p),…, s_n1(p) given both in magnitude and phase. These conditions reveal that the general problem is one of Nevalinna-Pick interpolation. Lastly, five worked examples are used to illustrate all facets of the theory.     

The compatibility of n-ports in parallel

A mathematical test for the compatibility of n-ports in parallel is given. It is shown that the well-known Brune tests are sufficient but not necessary.     

Synthesis of n-port active rc networks with a minimum number of capacitors

A new and practical synthesis procedure is presented for the realization of an arbitrary n × n matrix of real rational functions of the complex frequency variable as the short-circuit admittance matrix of a transformerless active RC n-port network. The realization requires a theoretically minimum number of capacitors p, where p is the degree of the matrix, and no more than (n + p + 1) grounded finite-gain phase-inverting voltage-controlled voltage sources. All the capacitors and ports are grounded. The freedom implicit in the synthesis procedure allows the inclusion of constraints on the passive element values. Furthermore, in special cases the realization is achieved with a reduced number of conductances and voltage-controlled voltage sources. The synthesis procedure is simple to apply and can readily be implemented on a digital computer. Several examples are given.     

A single‐stage integrated bridgeless AC/DC converter for electrolytic capacitor‐less LED lighting applications

In this paper, a single‐stage integrated bridgeless AC/DC converter is proposed. As compared to its counterpart that is composed of totem‐pole boost power factor correction (PFC) cascade fly‐back DC/DC converter, the studied circuit has less components number while overcoming the limits of the totem‐pole type. Thus, it is suitable to the low‐power LED lighting applications. Furthermore, when both PFC inductors L_b and magmatic inductance L_m of the transformer TR1 operate at discontinuous current mode, the bus voltage v_CB can be used to decouple the ac input and constant dc output power. Thus, the approach of increasing bus voltage ripple is employed to eliminate electrolytic capacitors and obtain long operation lifetime. Additionally, it is able to be compatible with our studied twin‐bus configuration for increasing the overall efficiency. A 50‐W hardware prototype has been designed, fabricated, and tested in the laboratory to verify the proposed converter validity. Copyright © 2014 John Wiley & Sons, Ltd.